Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients. 3x² – x – 4.

3x² – x – 4
= 3x² – 4x + 3x – 4
= x(3x – 4) + 1(3x – 4)
= (3x – 4)(x + 1)
The value of 3x² – x – 4 is zero if 3x – 4 0 or x + 1 0.
⇒ x = 4/3 or x = -1.
Therefore, the zeroes of 3x² – x – 4 are and -1.
Now, Sum of zeroes = 4/3 +(-1) = (4 – 3)/3 = 1/3 = -(-1)/3 = -(Coficient of x)/(Cofficient of x²)
Product of zeroes = 4/3 × (-1) = -4/3 = (-4)/3 = (Coefficient of term)/(Cofficient of x²)

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